Odriozola, 22, has won rave reviews for his displays with the San Sebastian club in La Liga.

His form on either side of defence even led to a surprise World Cup call-up for the full-back from former Roja coach Julen Lopetegui, although successor Fernando Hierro failed to give him a single minute on the field as Spain crashed out in the last 16.

La Real added in their own statement: "Real Sociedad want to thank Alvaro Odriozola for his professionalism and commitment shown to our club since his years as a youth player through to the first team, while also wishing him the best for his personal and professional future."

Odriozola is the first arrival in what promises to be a busy transfer window for Madrid, who were relatively inactive throughout Zinedine Zidane's two and a half years in the hotseat.

PSG duo Kylian Mbappe and Neymar, meanwhile, have both been slated as possible replacements for the Portugal legend, although with both still active in the World Cup Blancos fans may have to wait for further transfer updates.